Question

The national average SAT score (for verbal and math) is 1028. Suppose that nothing is known about the shape of the distribution and that the standard deviation is 100. Round the final answer to four decimal places and intermediate z-value calculations to two decimal places Source: New York Times Almanac. Part 1 out of 2 If a random sample of 245 scores was selected, find the probability that the sample mean is greater than 1041. Assume that the sample is taken from a large population and the correction factor can be ignored. P(X 1041)-

Answer 1

Solution:

Given, the unknown distribution with

= 1028

= 100

Sample of 245 is taken.

n= 245

Let be the sample mean.since sample is sufficient large ,we know the distribution of is normal with

Mean() = = 1028

SD() = = 100/​245 = 6.38876565

Find P(>1041)

P(>1041)= 1 - P(<1041)

=

1041-ni) 1 - P( Ơi

=   

7 1041 - 1028 6.38876565

= 1 - P(Z<2.03)

= 1 - 0.9788 .....use z table.

=   0.0212